[A4] Radio Noise

I have static or noise coming in on my factory radio (2001 A4), on the AM
band only. The noise comes and goes, but it's worse usually at night (when
the AM stations are weaker). It picks up a lot more when the rear defrost
is turned on. On top of the background noise, you can sometimes hear clicks
and pops as you step on the brakes, turn signals flashing, etc. The noise
is constant, not engine-speed related, so it's not something like an
alternator causing this noise.
I think due to the poor design of the antennae (lines on the back window)
that the AM signals being received are very weak to start with. That's why
Audi has an antennae booster located in the C-pillar, to boost the signal
before sending it to the radio. At first I thought this booster was to
blame, but they've changed both the booster, and the radio (for another
problem), with no change.
I'm pretty sure this is electrical interferrence from the car itself. If
you turn off the car completely, and just turn on the radio, there's no
noise. As soon as you turn the key to ON (without even starting the car),
the noise returns. And if you turn on some items (like rear defroster), it
gets worse.
I'm thinking that it's a Grounding issue, that either the Antennae or the
booster has a loose ground, or that they need a separate ground from other
components in the area. But I'm having a tough time convincing the
dealership that's the problem. I had suggested that they put some little
filters on the radio and booster power leads, but they say it won't make a
difference. They consulted the Audi techs, and the techs said to change the
booster, which didn't help.
I'm going in for my next scheduled service tomorrow, and I want them to fix
this noise before my warrantee is up in 2 months.
Has anyone else experienced any problems like this, and found some way to
correct it? What was your solution?
Thanks for your help.
Mitchell Segal